Method of anti-lock braking of a motorcycle and of determining the coefficient of adhesion

ABSTRACT

A method of determining the coefficient of adhesion between a roadway and the wheels of a motorcycle provides for retarding the rear wheel of the motorcycle more strongly than the front wheel for a predetermined period of time and for comparing the rotational speeds or the rotational retardations of the front and rear wheels. Furthermore, the sloping of the motorcycle is measured directly so as to determine both the longitudinal coefficient of adhesion and the lateral coefficient of adhesion from the sloping. The coefficients of adhesion thus obtained serve for adjustment of threshold values for anti-lock braking of the motorcycle.

BACKGROUND OF THE INVENTION

The invention relates to a method of anti-lock braking of a motorcycle,wherein the brake pressure in the brake of a front wheel or rear wheelis kept constant or reduced when the rotational retardation and/or slipof the wheel exceed a predetermined threshold value.

The invention further relates to a method of determining the coefficientof adhesion between a roadway and the wheels of a motorcycle, especiallythe determination of the longitudinal and lateral coefficients ofadhesion.

DESCRIPTION OF PRIOR ART

Different varieties of anti-lock brake systems for motorcycles are knownas such. With them, anti-lock brake systems (ABS) known for four-wheelvehicles are modified in consideration of the special characteristics ofa single-track, two-wheel vehicle.

Methods are known, with four-wheel vehicles, of obtaining a statement onthe instantaneous coefficient of adhesion between a wheel and theroadway by retarding that wheel more than another wheel for a briefmoment so as to derive a statement on the coefficient of adhesion fromthe slip of the more strongly retarded wheel. In this case it is assumedthat the driving stability of the four-wheel vehicle will not beimpaired by such a short-term disturbance. With a two-wheel vehicle, onthe other hand, that method would appear to be unsuited as both wheelsnecessarily have to remain stable.

SUMMARY OF THE INVENTION

The invention has for its aim to improve a conventional ABS brakingsystem for a motorcycle, at little expenditure, such that informationcan be obtained about the coefficient of adhesion between the wheels andthe roadway, on the one hand, and, on the other hand, the anti-lockcontrol is adjusted in accordance with the coefficient of adhesiondetermined.

According to a first embodiment of the invention first it is determinedif the motorcycle is in an inclined position, e.g. driving through acurve and, depending on the measured value of that sloping, either athreshold value of response for anti-lock control and/or a gradient ofpressure rise for anti-lock control corresponding to the value measuredof the sloping is set, this being done according to limited grading.Apart from the sloping of the motorcycle, also the transverseacceleration thereof may be determined by per se known means in order toadjust the anti-lock control. Adjustment in respect of the slopingand/or the transverse acceleration may be realized in predeterminedstages, especially three different stages. The response threshold valuesand/or the pressure increase gradients relating to the anti-lock controlmay be varied in three steps, depending on the degree of inclination orthe amount of transverse acceleration. And the response threshold valuesor the pressure increase gradients of the ABS control are set moresensitively with increasing sloping or transverse acceleration so thatthe retarded wheel can be caused to suffer a lower maximum slip uponbraking as the inclination or transverse acceleration becomes greater.

In accordance with the invention provision is made for determining thecoefficient of adhesion between the roadway and the wheels of themotorcycle by retarding the rear wheel of the motorcycle more than thefront wheel, for a given time span, and comparing the rotational speedsand/or the rotational retardations of the front and rear wheels so as toderive the coefficient of adhesion from the result of the comparison.

The invention is based on the finding that, for a short period of time,a motorcycle quite well may be retarded more strongly at the rear wheelthan at the front wheel without causing any considerable risk to thedriving stability, even when driving through a curve. That is distinctlyin contrast to the dynamics of four-wheel vehicles where overbraking ofthe rear wheels may generate a torque about the vertical axis, thusresulting in complete instability.

For braking during straightforward movement (without any sloping worthmentioning of the motorcycle) the slip between the rear wheel which isretarded somewhat more in the above manner and the front wheel is anunambiguous function of the coefficient of adhesion of that givenmotorcycle which is equipped with the prescribed tires and a givenloading (weight of the driver, passenger, baggage). This function with agiven loading can be memorized as a parameter in a computer (e.g. in theform of a table). The experimental data may be obtained from test runson an experimental course with different known coefficients of adhesion(measured in another known manner) and stored once and for all in thecomputer. The instantaneous loading of the motorcycle may be determinedby a simple force measurement and entered into the computer, e.g. duringslow forward driving. The computer thus will "know" the loading of themotorcycle and be able, upon braking, to determine the coefficient ofadhesion directly from the slip of the rear wheel which is retarded morethan the front wheel in defined manner, based on the data memorized. Inaccordance with a preferred embodiment of the invention that isaccomplished by the fact that in principle less pressure is fed into thebrakes of the front axle than into the brakes of the rear axle by way ofa mechanical pressure hold-back valve. The coefficient of adhesion thusdetermined either may be indicated to the driver or drawn upon directlyfor modification of the anti-lock control. The lower the coefficient ofadhesion (coefficient of friction), the more sensitive the adjustment ofthe ABS control must be, i.e. the threshold values of the anti-lockcontrol causing initiation of a reduction in pressure or maintenance ofa constant level of the pressure at the brake must be set moresensitively. The determination of the coefficient of adhesion betweenthe tire and the roadway in accordance with the invention permits betteranti-lock control due to the fact that, in accordance with the values ofahesion measured, the ABS pressure increase gradients and/or thethreshold values can be set in response to the values of adhesion.

In accordance with another preferred embodiment of the invention,therefore, only very low brake pressure (pressure just sufficient tocause engagement of the brakes) is supplied to the front axle brakes ofthe motorcycle in the so-called initial braking cycle (i.e. the firstcycle of an anti-lock control operation), while the brakes of the rearaxle are fed with relatively high brake pressure. In this mannerinformation about the coefficient of adhesion between tire and roadwaycan be obtained right at the beginning of an anti-lock brake controloperation, and subsequently the ABS control may be set for all thesuccessive control cycles in accordance with the coefficient of frictionmeasured. Specifically, an accurately tuned brake pressure may now beapplied to the brake at the front axle, based on the coefficient offriction measured.

Of special interest in braking a motorcycle are the so-calledlongitudinal and lateral coefficients of adhesion, in other words thecoefficients of friction, once in forward direction and, on the otherhand, perpendicular to the same. These two coefficients of friction aredecisive for the driving behavior of the motorcycle in inclinedposition, i.e. especially in a curve.

The invention provides a method of determining the instantaneouscoefficients of adhesion between the wheels of a motorcycle and theroadway when driving through a curve. To achieve that, at least thefollowing magnitudes are measured during a braking operation:

a) the wheel loads perpendicular and parallel to the roadway,

b) the brake torque, and

c) the wheel acceleration, and, if desired,

d) the sloping.

The longitudinal and lateral coefficients of adhesion are derived fromthe same.

The wheel loads vertically with respect to the roadway and parallel withrespect to the roadway (F_(N) and F_(S), respectively) are calculatedaccording to the invention by means of forces which are measurabledirectly at the motorcycle and the sloping angle.

The brake torque M_(B) for any given brake system results directly fromthe measurable brake pressure, assuming a typical coefficient offriction of the brake and a mean temperature. In accordance with arefinement of the invention the temperature of the friction linings maybe measured and the brake torque determined according to thetemperature. Once again, the brake torques belonging to the brake arefiled for good in the ABS computer in response to the brake pressure, ifdesired in dependence upon the temperature measured of the brakes, andthey are available in the computer later on for evaluation.

The rotational speeds and rotational retardations of the wheels aredetermined or calculated in conventional manner by means of the ABScomputer.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the invention will be explained further with referenceto the drawing, in which:

FIG. 1 is a diagrammatic presentation of a motorcycle in inclinedposition, of its center line, and of force vectors and angles essentialto the invention;

FIGS. 2a-2d are diagrammatic illustrations of the measurement of thesloping of the motorcycle;

FIG. 2a is a transmitted signal intensity-time diagram for measuringslope of a motorcycle when it is level;

FIG. 2b is an intensity-time diagram when a motorcycle is sloping in adirection wherein a receiver R₁ at one end of the motorcycle handle baris distal relative to a road surface;

FIG. 2c is a diameter similar to FIG. 2b when a second receiver R₂ atthe opposite end of the handle bar is proximal to the road surface; and

FIGS. 3a-3d are diagrammatic presentations of the longitudinal andlateral coefficients of adhesion, respectively, as a function of slip.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In literature the coefficient of adhesion μ to be determined accordingto the invention is referred to also as coefficient of friction orcoefficient of brake pressure, cf. for instance BOSCH TECHNISCHEBERICHTE, vol. 7, 1980, no. 2 (English special edition, February 1982,ISSN 0006-789X).

When a motorcycle is driving through a curve, i.e. when it is sloping itmakes sense, for ABS braking, to look at a coefficient of adhesion μ_(L)in longitudinal direction (driving direction, i.e. tangent to the curve)and a coefficient of adhesion μ_(S) in lateral direction (in other wordsvertically as regards the longitudinal direction, i.e. radially withrespect to the curve).

Due to Newton's axiom "rotational force=moment of inertia x rotationalacceleration" the following differential equation results for thelongitudinal coefficient of adhesion μ_(L) on the basis of physicalconsiderations (cf. the above mentioned BOSCH TECHNISCHE BERICHTE):##EQU1## The lateral coefficient of adhesion μ_(S) results by definitonfrom: ##EQU2## In the above equations: μ_(L) =coefficient of adhesion(coefficient of friction) in longitudinal direction;

μ_(S) =coefficient of adhesion in transverse direction;

Θ=rotational moment of inertia of the wheel (including vehicle partswhich are kinematically coupled to the wheel, depending on couplingcondition);

ω=wheel acceleration;

M_(B) =brake torque acting at the wheel;

F_(S) =wheel load parallel to the roadway (see FIG. 1);

F_(N) =wheel load perpendicular to the roadway (see FIG. 1);

R_(R) =wheel radius.

In the above equation of μ_(L) both Θ and R_(R) can be regarded as beingconstant for a given motorcycle and, therefore, can be firmly set fromthe beginning. The brake torque M_(B) is measurable, namely by measuringthe brake pressure which prevails in the brake and to which the braketorque corresponds in first approximation when second approximations,such as the temperature of the brake, the state of the friction liningsare neglected. If desired, the temperature of the brake may be measuredand its influence on the brake torque on the basis of experimental datalikewise be memorized in the computer so as to determine the associatedbrake torque in the computer on the basis of the prevailing brakepressure and temperature.

The wheel acceleration ω can be determined by means of rotational speedsensors in a manner known in the ABS art.

The wheel loads F_(N) and F_(S) can be determined by measuring forcesacting at the motorcycle and by measuring the sloping λ of themotorcycle. This is explained in FIGS. 1 and 2a.

FIG. 1 diagrammatically shows a tire R of a motorcycle on a roadway F,having a center line marked M. The motorcycle is in inclined position,its sloping angle λ being indicated with respect to the vertical V inFIGS. 1 and 2a. Due to the sloping, the point of contact P between thetire R and the roadway F travels away from the line of symmetry (centerline M), taking an asymmetric position, as shown in FIG. 1.

F_(A) and F_(B) are the forces acting at the left and right forks,respectively, on the wheel axle A (FIGS. 1 and 2a). These forces F_(A)and F_(B) can be determined by known force measuring devices, such asstrain gauge means etc. The situation is analogous with respect to theforce component F_(ax) which is vertical to the center line M, in otherwords the force acting on the wheel axle A perpendicular to the centerline M. This force acts between the fork and the axle.

Thus the force vectors F_(A), F_(B), and F_(ax) can be determined as tomagnitude.

The determination of the sloping angle λ likewise is required to findout the wheel loads F_(N) and F_(S). The arrangement shown in FIG. 2aserves that purpose, with parts corresponding to FIG. 1 being marked bythe same reference character. A transmitter T for ultrasonic waves isarranged centrally in the area of the wheel axle A to determine theinclined position. Receivers R₁ and R₂ spaced at distance a from thetransmitter T are disposed at either side of the center line M of themotorcycle. Ultrasonic waves emitted by the transmitter T are reflectedby the roadway F and received by the receivers R₁, R₂. The beams comingfrom the transmitter T and received by the receiver R₁ are marked S₁ inFIG. 2a, while the beams S₂ are reflected from the transmitter T to thereceiver R₂.

The ultrasonic beams S₁ and S₂ are emitted in pulsating fashion, and thetravelling times of the ultrasound to the individual receivers aremeasured. That is illustrated schematically in FIGS. 2b, 2c and 2d.

The intensities I of the signals are plotted above a common time scale tin FIGS. 2b, 2c and 2d.

FIG. 2b shows the intensity of the signal pulse emitted by thetransmitter T. If the motorcycle is not sloping, i.e. if the angle λ is0°, both receivers R₁ and R₂ will receive the signal after the same timet₀. The corresponding pulses are drawn in FIGS. 2c and 2d. When themotorcycle is at an inclination of sloping angle λ, receiver R₁ willreceive the signal offset by a period of time t due to the greaterdistance.

The instantaneous velocity of sound c for the associated atmosphericmoisture prevailing at the particular moment can be determined by meansof time period t₀ since the travelilng distance results directly fromthe geometric conditions. The sloping angle λ is a function of thedifference in time t. This function may be filed in the computer, eitheranalytically as a function or as a truth table. Thus all the determiningmagnitudes are given for finding out the wheel loads F_(N) and F_(S).Geometric considerations result in the following equations for the wheelloads:

    F.sub.S =F.sub.A sin λ+F.sub.B sin λ-F.sub.ax cos λ

    F.sub.N =F.sub.A cos λ+F.sub.B cos λ+F.sub.ax sin λ

The computer thus determines the wheel loads F_(S) and F_(N) anddirectly from them the lateral coefficient of adhesion μ_(S) =F_(S)/F_(N), starting from the measured data.

Furthermore the computer determines the longitudinal coefficient ofadhesion μ_(L) from the differential equation given above of which allthe determinants likewise are known.

The determination described above of the coefficient of adhesion is afirst embodiment of the invention. It may be realized selectively withthe front wheel and, preferably, also with the rear wheel or with bothwheels.

Conventional motorcycle ABS control can be improved with the aid of thelongitudinal and/or lateral coefficients of adhesion thus determined inthat the threshold values for initiating a reduction in pressure or formaintaining the pressure constant are adjusted according to thecoefficients of adhesion measured. The lower the coefficients ofadhesion are, the more sensitive the threshold values must be set. Thelateral coefficient of adhesion determined according to the inventioncorresponds to the lateral guiding force at the tires of the motorcycle.

Another embodiment according to the invention for determining thecoefficient of adhesion provides for retarding the rear wheel somewhatmore than the front wheel. In contrast to four-wheel vehicles this ismuch less critical with two-wheel vehicles. In accordance with theinvention, according to FIG. 3, the coefficient of brake pressure μ(coefficient of adhesion) of the rear wheel is increased by a certainrelatively small amount μ_(L) as compared to the coefficient of brakepressure prevailing at the front wheel. That is demonstrated in FIG. 3ain the usual presentation of a coefficient of brake pressure/slip curve.The slip S is entered on the abscissa.

In FIG. 3a-d the coefficients of brake pressure of the front wheel eachare illustrated by an empty circle and those of the rear wheel by asolid circle.

If the coefficient of brake pressure μ_(L) of the rear wheel is raisedby the value μ_(L) the slip with respect to the front wheel changes bythe amount S (FIG. 3a).

FIG. 3b shows the lateral coefficient of brake pressure under the samecircumstances as in FIG. 3a. The lateral coefficient of brake pressure(also called coefficient of lateral force) diminishes at increasingslip, as is known and illustrated in FIG. 3b by the continuous line (cf.e.g. the above mentioned BOSCH TECHNISCHE BERICHTE or the paper by H.Laiber and W.D. Limpert in AUTOMOBILTECHNISCHE ZEITSCHRIFT, Juni 1969,page 181 et seqq.).

In FIGS. 3a and 3b the relative augmentation of the brake pressure atthe rear wheel as compared to the brake pressure at the front wheelbegins relatively soon, i.e. far within the stable range of thecoefficient of brake pressure/slip curve, i.e. far to the left ofmaximum μ_(Lmax). For this reason the coefficients of lateral forceμ_(S) of the front and rear wheels remain the same according to FIG. 3bsince the system is clearly within the so-called Kummer's circle (cf.e.g. the journal quoted above: AUTOMOBILTECHNISCHE ZEITSCHRIFT, FIG. 2).In FIG. 3b the formula μ_(s) =v /R×g means the conversion of the formulafor the centrifugal force according to the coefficient of lateraladhesion, with v being the vehicle speed, R the radius of the curve, andg the acceleration due to gravity.

The conditions are different in FIGS. 3c and 3d. There the pressureincrease in the brake of the rear wheel begins much closer to themaximum of the coefficient of brake pressure/slip curve (FIG. 3c) sothat the lateral guiding force of the rear wheel drops according to FIG.3d. The systems reaches the limits, predetermined by Kummer's circlementioned above, as regards the longitudinal coefficient of brakepressure μ_(L) and the lateral coefficient of brake pressure μ_(S)(lateral guiding force). According to FIG. 3d, therefore, in this casealso a difference μ_(S) occurs between the front and rear wheels. Thisdifference μ_(S) can be determined based on the measurement describedabove of μ_(S). It indicates that the rear wheel should not be subjectedany longer to higher pressurization but that instead its pressure shouldbe lowered again together with the brake pressure of the front wheeluntil the difference μ_(S) disappears and the system once more complieswith the conditions according to FIGS. 3a and 3b.

The interplay described above of increasing the brake pressure at therear wheel as compared to the brake pressure at the front wheel toproduce the difference μ_(L) and the associated observation of thedifference μ_(S) permits new ABS braking of motorcycles. The brakepressure at the rear wheel is raised by a predetermined amount ascompared to the brake pressure at the front wheel so that thecoefficient of adhesion of the rear wheel in each instance is greater bythe difference μ_(L) than that of the front wheel. Stable conditions ofthe wheels are assumed, i.e. the system is to the left of the maximum ofthe coefficient of friction/slip curve (FIGS. 3a, c). This raising iscontinued for as long as the lateral coefficient of adhesion μ_(S) ofthe rear wheel equals the lateral coefficient of adhesion μ_(S) of thefront wheel (FIG. 3b). If, on the other hand, a difference occursbetween the lateral coefficients of adhesion μ_(S) of the front and rearwheels that is an indication of the fact that the brake pressure hasreached a maximum value and that consequently the brake pressures in thebrakes of the front and rear wheels must be lowered at the same timeuntil the difference in respect of the lateral coefficients of adhesionμ_(S) disappears. It is understood that the value μ_(L) is not increasedbeyond the maximum value μ_(Lmax) (FIG. 3a).

What is claimed is:
 1. A method of anti-lock braking of a motorcyclehaving front and rear wheels each having a brakes, comprising the stepsof:a) applying braking pressure to said front and rear wheel brakes, b)measuring the value of rotational retardation and slip of the frontwheel and the rear wheel of the motorcycle, c) comparing the value ofthe measured rotational retardation and slip of the front and rearwheels with a predetermined threshold value, d) maintaining or reducingsaid braking pressure when said measured value exceeds a predeterminedthreshold value, e) applying for a predetermined period of time to thebrake of the rear wheel a higher brake pressure than to the brake of thefront wheel, f) comparing, at the time when a higher brake pressure isapplied to the brake of the rear wheel than to the brake of the frontwheel, rotational speeds and rotational retardations of the front andthe rear wheels, and g) adjusting said threshold value in response tosaid comparison.
 2. A method of determining a coefficient of adhesionbetween a roadway and wheels of a motorcycle, the motorcycle having afront and a rear wheel each wheel having a brake, comprising the stepsof:a) applying to the brake of the rear wheel of the motorcycle a brakepressure such that the rear wheel is retarded more than the front wheelfor a predetermined period of time, b) comparing, at the time when therear wheel is retarded more than the front wheel, rotational speeds ofthe front and the rear wheels, and c) deriving said coefficient ofadhesion from the result of said comparison.
 3. A method of anti-lockbraking of a motorcycle having front and rear wheels each provided withbrakes, comprising the steps of:a) measuring a value of rotationalretardation and slip of the front wheel and the rear wheel of themotorcycle, b) comparing the measured value of rotational retardationand slip of the front and rear wheels with a threshold value in order toderive control signals for said anti-lock braking, c) applying to thebrakes of the rear wheel of the motorcycle a brake pressure such thatthe rear wheel is retarded more than the front wheel for a predeterminedperiod of time, d) comparing, at the time when the rear wheel isretarded more than the front wheel rotational speeds of the front andthe rear wheels, e) deriving a coefficient of adhesion from the resultof said comparison, and f) adjusting said threshold value in accordancewith said derived coefficient of adhesion.
 4. The method as claimed inany one of the preceding claims, characterized in that, in addition aslope of the motorcycle relative to a surface on which it is travelingis measured.